Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Sunday, October 22, 2006

FOCS Begins

Weblog correspondent Janos Simon reports from Berkeley.

This is a pre-FOCS FOCS report, filling in for Lance.

FOCS 2006 is at Berkeley
Marina, a lovely place on the Bay, with expensive sailboats next to
the hotel gardens, against the beautiful backdrop of the San Francisco
Bay, with the Berkeley hills on the other side. All of this even
comes at a relatively cheap price.

Unfortunately the hills of Berkeley are not so near: downtown Berkeley
is about 3 miles from the hotel, on the other side of train tracks and the
interstate. This not only prevents one from easily strolling
around the Berkeley campus and stopping at one of the nice coffeehouses or
bookstores, but also makes getting dinner more of an adventure, involving a
cab or a hotel shuttle.
I am not complaining about the organizers:
putting a conference together is a difficult balancing act, with too many
constraints.

The conference itself should be excellent, with very strong papers,
including the
solution of the 2-player Nash equilibrium that won the best paper
award. There will be three invited talks, all dealing in one way or
other with Theory interacting with other areas of knowledge: tomorrow
(Sunday) Karp will talk about "Theory of Computation as a Lens on
the Sciences", Monday Terry Senjowski will teach us about Vision,
and Tuesday Jon Kleinberg will discuss networks, social and
technological. The biggest innovation relative to previous FOCS will
be the presentation of Lady X and the Positive Eigenvalues, a rock
concert. [For those with a historical bug, this is not an absolute
first. Dexter Kozen, with Anna Karlin of the Severe Tire Damage rock
band—the first to broadcast a rock concert on the
internet—have in the past help expand our horizons in these
directions, I believe at the Palo Alto conference, but I cannot offer
precise pointers.]

The conference has parallel sessions (pros and cons have been
previously and exhaustively discussed), so I will only be able to
provide a very incomplete report of the papers presented. I should
also add that I expect to miss many talks, not only due to my
non-quantum nature and consequent lack of ability to be in two places
at the same time, but also due to random phenomena: sleeping late,
meeting friends, discussing ideas, wandering into the wrong lecture
room, and forgetting about the time of talks I wanted to hear. So the
papers I'll mention are not necessarily the ones I chose to
listen to, just the ones I happened to not miss, and inferences about
my taste or the quality of papers ignored would likely be mistaken.

Given that caveat, I can talk about two very nice results to be presented
today. I heard them at Chicago before the conference.

The first is Tom Hayes' paper that gives a sufficient condition for
certain important probabilistic models to converge rapidly. For
definitions, technical details, etc read the paper. What I liked is
that the paper is not only a significant technical improvement, but
this seems to be the "correct" reason that lurked behind
previous proofs, and this (I think) will be the proof we will teach.

The second is the paper by
Belkin, Narayanan and Niyogi on estimating
the surface area of a convex body. Both the area and the volume of
high-dimensional convex bodies are very hard to approximate by the
"natural" method of approximating the boundary by a simple smooth
object: the number of parameters to do so grows too fast. For the
volume, one can use random walks: an appropriate random walk on the
space is stopped and we record whether we stopped inside or outside
the object. The ratio of these events can be used to estimate the
volume. Unfortunately this does not work for the surface area. The
very cute idea of the Belkin et al paper is to put a heat source
inside the object, and observe the amount of heat that leaks outside:
this will be proportional to the area

Of course there are lots of technical difficulties, but they can be overcome.
The details are not easy, but I thought the idea was new and nice.

3 comments:

I recall that Dexter and his band performed at the Monterey aquarium during LICS 1989. Amongst others, they offered (T)CS renditions of songs by the Ramones (I wanna be promoted) and the Dead Kennedys (Categories uber alles). At the time I collected a leaflet with the text of the songs Dexter's band played, but I seem to have lost it. The band played well, and the songs were a lot of fun to listen to. I'd love to get my hands on the text of the songs again.